uncertainty assessment of a dominant-process catchment model … · tural headwater catchments. the...

Hydrol. Earth Syst. Sci., 20, 4819–4835, 2016www.hydrol-earth-syst-sci.net/20/4819/2016/doi:10.5194/hess-20-4819-2016© Author(s) 2016. CC Attribution 3.0 License.

Uncertainty assessment of a dominant-process catchment model ofdissolved phosphorus transferRémi Dupas1, Jordy Salmon-Monviola1, Keith J. Beven2, Patrick Durand1, Philip M. Haygarth2,Michael J. Hollaway2, and Chantal Gascuel-Odoux1

1INRA, Agrocampus Ouest, UMR1069 SAS, 35000 Rennes, France2Lancaster Environment Centre, Lancaster University, Lancaster, LA1 4YQ, UK

Correspondence to: Rémi Dupas ([email protected])

Received: 17 December 2015 – Published in Hydrol. Earth Syst. Sci. Discuss.: 19 January 2016Revised: 11 August 2016 – Accepted: 7 November 2016 – Published: 8 December 2016

Abstract. We developed a parsimonious topography-basedhydrologic model coupled with a soil biogeochemistry sub-model in order to improve understanding and predictionof soluble reactive phosphorus (SRP) transfer in agricul-tural headwater catchments. The model structure aims tocapture the dominant hydrological and biogeochemical pro-cesses identified from multiscale observations in a researchcatchment (Kervidy–Naizin, 5 km2). Groundwater fluctua-tions, responsible for the connection of soil SRP productionzones to the stream, were simulated with a fully distributedhydrologic model at 20 m resolution. The spatial variabilityof the soil phosphorus content and the temporal variabilityof soil moisture and temperature, which had previously beenidentified as key controlling factors of SRP solubilizationin soils, were included as part of an empirical soil biogeo-chemistry sub-model. The modelling approach included ananalysis of the information contained in the calibration dataand propagation of uncertainty in model predictions using ageneralized likelihood uncertainty estimation (GLUE) “lim-its of acceptability” framework. Overall, the model appearedto perform well given the uncertainty in the observationaldata, with a Nash–Sutcliffe efficiency on daily SRP loadsbetween 0.1 and 0.8 for acceptable models. The role of hy-drological connectivity via groundwater fluctuation and therole of increased SRP solubilization following dry/hot peri-ods were captured well. We conclude that in the absence ofnear-continuous monitoring, the amount of information con-tained in the data is limited; hence, parsimonious models aremore relevant than highly parameterized models. An analysisof uncertainty in the data is recommended for model calibra-tion in order to provide reliable predictions.

1 Introduction

Excessive phosphorus (P) concentrations in freshwater bod-ies result in increased eutrophication risk worldwide (Car-penter et al., 1998; Schindler et al., 2008). Eutrophicationrestricts economic use of water and poses a serious hazardto ecosystems and humans (Serrano et al., 2015). In westerncountries, reduction of point-source P emissions in the last2 decades has resulted in a proportionally increasing contri-bution of diffuse sources, mainly from agricultural origins(Alexander et al., 2008; Grizzetti et al., 2012; Dupas et al.,2015a). Of particular concern are dissolved P forms, oftenmeasured as soluble reactive phosphorus (SRP) because theyare highly bioavailable and therefore a likely contributor toeutrophication.

To reduce SRP transfer from agricultural soils, it is im-portant to identify the spatial origin of P sources in agri-cultural landscapes, the biogeochemical mechanisms causingSRP solubilization in soils and the dominant transfer path-ways, as well as the potential P resorption during transit.Research catchments provide useful data to investigate SRPtransport mechanisms: typically, the temporal variations inwater quality parameters at the outlet, together with hydro-climatic variables, are investigated to infer spatial origin anddominant transfer pathways of SRP (Haygarth et al., 2012;Outram et al., 2014; Dupas et al., 2015b; Mellander et al.,2015; Perks et al., 2015). Hypotheses drawn from analysis ofwater quality time series can be further investigated throughhillslope monitoring and/or laboratory experiments (Heath-waite and Dils, 2000; Siwek et al., 2013; Dupas et al., 2015c).When dominant processes are considered reasonably known,

Published by Copernicus Publications on behalf of the European Geosciences Union.

4820 R. Dupas et al.: Phosphorus transfer modelling

it is possible to develop computer models, for two main pur-poses. First, to validate scientific conceptual models one cantest whether model predictions can produce reasonable simu-lations compared to observations. Of particular interest is thepossibility of testing the capability of a computer model toupscale P processes observed at fine spatial resolution (soilcolumn, hillslope) to a whole catchment. Second, if the mod-els survive such validation tests, they can be useful tools tosimulate the response of a catchment system to a future per-turbation such as changes in agricultural management andclimate changes.

However, process-based P models generally performpoorly compared to, for example, nitrogen models (Wade etal., 2002a; Dean et al., 2009; Jackson-Blake et al., 2015).This is of major concern because poor model performancesuggests poor knowledge of dominant processes at the catch-ment scale, and poor reliability of the modelling tools used tosupport management. The origin of poor model performancemight be conceptual misrepresentations, structural imperfec-tion, calibration problems, irrelevant model evaluation cri-teria and difficulties in properly assessing the informationcontent of the available data when it is subject to epistemicerror. All five causes of poor model performance are inter-twined; e.g. model calibration strategy depends on modelperformance evaluation criteria, which depend on the waythe information contained in the observation data is assessed(Beven and Smith, 2015).

A key issue in environmental modelling is the level ofcomplexity one should seek to incorporate in a model struc-ture. Several existing P transfer models, such as INCA (Wadeet al., 2002a), SWAT (Arnold et al., 1998) and HYPE (Lind-strom et al., 2010) seek to simulate many processes, withthe view that complex models are necessary to understandprocesses and to predict the likely consequences of land useor climate changes. However, these complex models includemany parameters that need to be calibrated, while the amountof data available for calibration is often low. An imbalancebetween calibration requirement and the amount of avail-able observation data can lead to equifinality issues, i.e. whenmany model structures or parameter sets lead to acceptablesimulation results (Beven, 2006). A consequence of equifi-nality is the risk of unreliable prediction when an “optimal”set of parameters is used (Kirchner, 2006), and large uncer-tainty intervals when Monte Carlo simulations are performed(Dean et al., 2009). In this situation, it will be worth ex-ploring parsimonious models that aim to capture the domi-nant hydrological and biogeochemical processes controllingSRP transfer in agricultural catchments. For example, Hahnet al. (2013) used a soil-type-based rainfall–runoff model(Lazzarotto et al., 2006) combined with an empirical modelof soil SRP release derived from rainfall simulation experi-ments over soils with different P content and manure appli-cation level/timing (Hahn et al., 2012) to simulate daily SRPload from critical sources areas.

A second key issue, linked to the question of model com-plexity, concerns model calibration and evaluation. Both cal-ibration and evaluation require assessing the fit of model out-puts with observation data. However, observation data aregenerally not directly comparable with model outputs, be-cause of incommensurability issues and/or because they con-tain errors (Beven, 2006, 2009). Typically, predicted dailyconcentrations and/or loads are evaluated against data fromgrab samples collected on a daily or weekly basis. The in-formation content of these data must be carefully evaluatedto propagate uncertainty in the data into model predictions(Krueger et al., 2012). Uncertainty in grab sample data mightstem from (i) sampling frequency problems or (ii) measure-ment problems (Lloyd et al., 2016). Grab sample data repre-sent a specific point in the stream cross section, which candiffer from the cross section mean concentration (Rode andSuhr, 2007), and a snapshot of the concentration at a giventime of the day, which can differ from the flow-weightedmean daily concentration (McMillan et al., 2012). This dif-ference between observation data and simulation output canbe large during storm events in small agricultural catchments,as P concentrations can vary by several orders of magnitudeduring the same day (Heathwaite and Dils, 2000; Sharpley etal., 2008). Model evaluation can be severely hindered by thisdifference, because many popular evaluation criteria such asthe Nash–Sutcliffe efficiency (NSE) are sensitive to extremevalues and errors in timing (Moriasi et al., 2007). Duringbaseflow periods, it is more likely that grab sample data arecomparable to flow-weighted mean daily concentrations, asconcentrations vary little during the day and they are usu-ally low in the absence of point sources. However, measure-ment errors are expected to occur at low concentrations, ei-ther due to too long storage times or laboratory imprecisionwhen concentrations come close to detection/quantificationlimits (Jarvie et al., 2002; Moore and Locke, 2013). Uncer-tainty in the data can also relate to discharge measurementand input data (e.g. maps of soil P content and rainfall data).In this paper we strive to identify and quantify the differentsources of uncertainty in the data when the required qualitycheck tests have been performed (on the discharge and SRPconcentration data). A generalized likelihood uncertainty es-timation (GLUE) “limits of acceptability” approach (Beven,2006; Beven and Smith, 2015) is used to calibrate/evaluatethe model.

This paper presents a dominant-process model that cou-ples a topography-based hydrologic model with a soil bio-geochemistry sub-model able to simulate daily discharge andSRP loads. The dominant processes included in the hydro-logic and soil biogeochemistry sub-models have been iden-tified in previous analyses of multiscale observational data,which have demonstrated, on the one hand, the control ofgroundwater fluctuation on connecting soil SRP productionzones to the stream (Haygarth et al., 2012; Jordan et al.,2012; Dupas et al., 2015b, d; Mellander et al., 2015), and,on the other hand, the role of antecedent soil moisture and

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R. Dupas et al.: Phosphorus transfer modelling 4821

Figure 1. Soil drainage classes in the Kervidy–Naizin catchment (Curmi et al. 1998).

temperature conditions on SRP solubilization in soils (Turnerand Haygarth, 2001; Blackwell et al., 2009; Dupas et al.,2015c). Model development and application were performedin the Kervidy–Naizin catchment in western France with theobjectives of (i) testing if the model was capable of captur-ing daily variation of SRP load, thus confirming hypotheseson dominant processes; and (ii) developing a methodologyto analyse and propagate uncertainty in the data into modelprediction using a “limits of acceptability” approach.

2 Material and methods

2.1 Study catchment

2.1.1 Site description

Kervidy–Naizin is a small (4.94 km2) agricultural catchmentlocated in central Brittany, western France (48◦ N, 3◦W). Itbelongs to the AgrHyS environmental research observatory(http://www6.inra.fr/ore_agrhys_eng), which studies the im-pact of agricultural activities and climate change on waterquality (Molenat et al., 2008; Aubert et al., 2013; Salmon-Monviola et al., 2013; Humbert et al., 2015). The catch-ment (Fig. 1) is drained by a stream of second Strahler or-der, which generally dries up in August and September. Theclimate is temperate oceanic, with mean± standard devia-tions of annual cumulative precipitation and specific dis-charge of 854± 179 and 290± 106 mm respectively, from2000 to 2014. Mean annual± standard deviation of temper-ature is 11.2± 0.6 ◦C. Elevation ranges from 93 to 135 mabove sea level. Topography is gentle, with maximum slopesnot exceeding 5 %. The bedrock consists of impervious, lo-cally fractured Brioverian schists and is capped by severalmetres of unconsolidated weathered material and silty, loamysoils. The hydrological behaviour is dominated by the de-

velopment of a water table that varies seasonally along thehillslope. In the upland domain, consisting of well-drainedsoils, the water table remains below the soil surface through-out the year, varying in depth from 1 to > 8 m. In the wet-land domain, developed near the stream and consisting ofhydromorphic soils, the water table is shallower, remainingnear the soil surface generally from October to April eachyear. The land use is mostly agriculture, specifically arablecrops and confined animal production (dairy cows and pigs).A farm survey conducted in 2013 led to the following landuse subdivisions: 35 % cereal crops, 36 % maize, 16 % grass-land and 13 % other crops (rapeseed, vegetables). Animaldensity was estimated as high as 13 livestock units ha−1 in2010. Estimated soil P surplus was 13.1 kg P ha−1 yr−1 (Du-pas et al., 2015b) and soil extractable P in 2013 (Olsen etal., 1954) was 59± 31 mg P kg−1 (n= 89 samples). A surveytargeting riparian areas highlighted the legacy of high soilP content in these currently unfertilized areas (Dupas et al.,2015c). No point-source emissions were recorded, but scat-tered dwellings with septic tanks were present in the catch-ment.

2.1.2 Hydroclimatic and chemical monitoring

Kervidy–Naizin was equipped with a weather station (CimelEnerco 516i) located 1.1 km from the catchment outlet. Itrecorded hourly precipitation, air and soil temperatures, airhumidity, global radiation, wind direction and speed, whichare used to estimate Penman evapotranspiration. Streamdischarge was estimated at the outlet with a rating curveand stage measurements from a float-operator sensor (Thal-imèdes OTT) upstream of a rectangular weir.

To record both seasonal and within storm dynamics inSRP concentration, two monitoring strategies complementedeach other from October 2013 to August 2015: a daily man-

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ual grab sampling at approximately the same time (between16:00 and 18:00 local time) and automatic high-frequencysampling during 14 storm events (Teledyne autosamplerISCO 6712 Full-Size Portable Sampler; 24 1 L bottles filledevery 30 min). The water samples were filtered on-site, im-mediately after grab sampling and after 1–2 days in the caseof autosampling. They were analysed for SRP (ISO 15681)within a fortnight. To assess uncertainty in daily SRP concen-tration related to sampling time, storage and measurement er-rors, a second grab sample was taken at a different time of theday (between 11:00 and 15:00 local time) in 36 instances dur-ing the study period. The second sample was analysed within24 h with the same method; this second data set is referred toas verification data set, as opposed to the reference data set.Among the 36 pairs of comparable daily samples, 12 weretaken during storm events and 24 during baseflow periods.To assess uncertainty in high-frequency SRP concentrationduring storm events due to delayed filtration of autosamplerbottles, five grab samples were taken during the course offour distinct storms and were filtered immediately. The samelab procedure was used to analyse SRP.

2.1.3 Identification of dominant processes frommultiscale observations

Observations in the Kervidy–Naizin catchment have high-lighted that the temporal variability in stream SRP concen-trations could not be related to the calendar of agriculturalpractices but rather to hydrological and biogeochemical pro-cesses (Dupas et al., 2015b). The primary control of hy-drology on SRP transfer has also been evidenced in sev-eral other small agricultural catchments (e.g. Haygarth et al,2012; Jordan et al., 2012; Mellander et al., 2015). In theKervidy–Naizin catchment, the groundwater fluctuation invalley bottom areas was identified as the main driving fac-tor of SRP transfer, through the hydrological connectivity itcreates when the saturated zone intercepts shallow soil layers(Dupas et al., 2015b).

In situ monitoring of soil pore water at four sites (15 and50 cm depths) in the Kervidy–Naizin catchment has shownthat mean SRP concentration in soils is a linear functionof Olsen P (Olsen et al., 1954). This reflects the currentknowledge that a soil P test, or alternatively estimation ofa degree of P saturation, can be used to assess solubiliza-tion in soils (Beauchemin and Simard, 1999; McDowell etal., 2002; Schoumans et al., 2015). This linear relationshipderived from the data contrasts however with other studies,where threshold values above which SRP solubilization in-creases greatly have been identified (Heckrath et al., 1995;Maguire and Sims, 2002).

SRP solubilization in soil varies seasonally according toantecedent conditions of temperature and soil moisture. Dryand/or hot conditions are favourable to the accumulation ofmobile P forms in soils, while water-saturated conditions

lead to their flushing (Turner and Haygarth, 2001; Blackwellet al., 2009; Dupas et al., 2015c).

2.2 Description of the Topography-based NutrientTransfer and Transformation – Phosphorus model(TNT2-P)

TNT2 was originally developed as a process-based and spa-tially explicit model simulating water and nitrogen fluxes at adaily time step (Beaujouan et al., 2002) in meso-scale catch-ments (< 50 km2). TNT2-N has been widely used for opera-tional objectives, to test the effect of mitigation options pro-posed by local stakeholders or public policymakers (Moreauet al., 2012; Durand et al., 2015), on nitrate fluxes and con-centrations in rivers.

TNT2-P uses a modified version of the hydrological sub-model in TNT2-N, to which a P biogeochemistry sub-modelwas added to simulate SRP solubilization in soils.

2.2.1 Hydrological sub-model

The assumptions in the hydrological sub-model are derivedfrom TOPMODEL, which has previously been applied to theKervidy–Naizin catchment (Bruneau et al., 1995; Franks etal., 1998). (1) The effective hydraulic gradient of the satu-rated zone is approximated by the local topographic surfacegradient (tanβ). It is calculated in each cell of a digital el-evation model (DEM) at the beginning of the simulation.(2) The effective downslope transmissivity (parameter T ) ofthe soil profile in each cell of the DEM is a function of thesoil moisture deficit (Sd). Hydraulic conductivity is assumedto decrease exponentially with depth (parameter m, Fig. 2).Hence, water fluxes (q) are computed as

q = T · tanβ · exp(−Sd

m). (1)

Based on these assumptions, TNT2 computes an explicitcell-to-cell routing of fluxes, using a D8 algorithm.

To simulate SRP fluxes, the hydrological sub-model isused to compute water fluxes from each soil layer by inte-grating Eq. (1) between the maximum depth of the soil layerconsidered and either

– estimated groundwater level, if the groundwater table iswithin the soil layer considered,

or

– the minimum depth of the soil layer considered, if thegroundwater table above the soil layer considered.

In this application of the TNT2-P model, five soil layers witha thickness of 10 cm are considered. Hence, seven flow com-ponents are computed in the model:

– overland flow on any saturated surfaces;

– five sub-surface flow components, one for each soillayer;



Figure 2. Description of soil hydraulic properties and phosphoruscontent with depth.

– deep flow, i.e. flow below the five soil layers.

2.2.2 Soil P sub-model

The soil P sub-model is empirically derived from soil porewater monitoring data (Dupas et al., 2015c), specifically as-suming that

– the background SRP concentration in the soil pore waterof a given layer is proportional to soil Olsen P;

– seasonal increases in P availability compared to back-ground conditions are determined by biogeochemicalprocesses, controlled by antecedent temperature andsoil moisture. Data show that SRP availability in thesoil pore water increases following periods of dry andhot conditions (Dupas et al., 2015c).

Hence, SRP transfer is modelled with parameters that de-scribe both mobilization and transfer to the stream. A differ-ent parameter is used to simulate transfer via overland flowand sub-surface flow.

FSRP overland = CoefSRP overland · POlsen · qoverland, (2)FSRP sub-surface = CoefSRP sub-surface · POlsen · qsub-surface, (3)

where FSRP overland and FSRP sub-surface are SRP transfer viaoverland flow and sub-surface flow for a given soil layer re-spectively, qoverland and qsub-surface are water flows from thesame pathways. CoefSRP overland and CoefSRP sub−surface arecoefficients that vary according to antecedent temperatureand soil moisture conditions, such as

CoefSRP = Coefbackground · (1+FT ·FS), (4)

where CoefSRP is either CoefSRP overland orCoefSRP sub−surface, and FT and FS are temperature andsoil moisture factors, respectively. FT and FS are expressed

as

FT = exp(mean(temperature, i days)− T 1

T 2), (5)

FS = 1−(

mean(water content, i days )maximum water content

)S1

, (6)

where T 1, T 2 and S1 are parameters to be calibrated. Theantecedent condition time length consists in a period ofi = 100 days. Both soil temperature and soil moisture are es-timated by the TNT2 soil module (Moreau et al., 2013). Be-cause soil moisture in the deep soil layers can differ signifi-cantly from that of shallow soil layers, two values of FS arecalculated for two soil depth ranges: 0–20 and 20–50 cm. Thetemperature factor FT was calculated as an average value forthe entire 0–50 cm soil profile. Contrary to the water fluxes,SRP fluxes are not routed cell-to-cell because we lack knowl-edge of the rate of SRP re-adsorption in downslope cells andof the long-term fate of re-adsorbed SRP. Hence, all the SRPemitted from each cell through overland flow and sub-surfaceflow reaches the stream on the same day. For deep flow, onlythe immediate riparian flux is used in determining SRP in-puts to the river.

No long-term depletion of the different P pools was mod-elled, because annual P export from the catchment was smallcompared to the size of soil and sub-soil P pools.

2.2.3 Input data and parameters

Spatial input data required for TNT2-P include

– A DEM in raster format. Here, a 20 m resolution DEMwas used; hence, model calculations were made in12 348 grid cells covering a 4.94 km2 catchment.

– A map of soil units that could be assumed to have homo-geneous hydrological parameter values, in raster format.Here, two soil classes were considered by differentiat-ing well-drained (86 %) and poorly drained soils (14 %)according to Curmi et al. (1998) (Fig. 1). Experimentaldetermination of saturated hydraulic conductivity (29soil cores) by Curmi et al. (1998) showed significantlydifferent values for soils classified as well-drained andpoorly drained in the Kervidy–Naizin catchment. Thetwo units were treated as homogeneous, lacking infor-mation about the detailed variability in soil hydrauliccharacteristics at the model grid scale.

– A map of surface Olsen P in raster format and descrip-tion of decrease in the Olsen P with depth for five soillayers between 0 and 50 cm. Here, the map of OlsenP in the 0–15 cm soil layer was obtained from statisti-cal modelling with the rule-based regression algorithmCUBIST (Quinlan, 1992) using data from 198 soil sam-ples (2013) in an area of 12 km2 encompassing the4.94 km2 catchment (Matos-Moreira et al., 2015). Todescribe how Olsen P decreases with depth, land use



information was used. In tilled fields, i.e. all crop rota-tions including arable crops, Olsen P was assumed to beconstant between 0 and 30 cm and to decrease linearlywith depth between 30 and 50 cm. In no-till fields, i.e.permanent pasture and woodland, Olsen P was assumedto decrease linearly with depth between 0 and 50 cm.An exponential decrease with depth is more commonlyadopted in untilled land (e.g. Haygarth et al., 1998; Pageet al., 2005), but a specific sampling in currently un-tilled areas in the Kervidy–Naizin catchment (Dupas etal., 2015c) has shown that a linear function is more ap-propriate, probably because of these areas having beenploughed in the past. A previous study has shown thatsoil Olsen P was the most important factor controllingSRP solubilization in soils of the Kervidy–Naizin catch-ment (see Sect. 2.1.3); therefore, other parameters in thesoil P sub-model (Sect. 2.2.2) were treated as homoge-neous in the catchment (the soil classification into well-drained and poorly drained soils only concerned hydro-logical parameters).

A 20 m resolution was chosen for the DEM and the soilOlsen P raster map to allow for a detailed representation ofthe interaction of the groundwater table (as simulated by thehydrological model) and the soil Olsen P (as given by thesoil Olsen P map). Indeed the soil saturation and soil OlsenP can be very different in a narrow zone close to the streamcompared to upslope due to the presence of a 5 to 50 m unfer-tilized buffer zone with lower Olsen P compared to fertilizedfields. The Olsen P value close to the stream has a determin-ing influence on SRP transfer, because this area is the mostfrequently connected to the stream; therefore, a coarser reso-lution of the raster maps would degrade representation of thesystem.

Climate input data include minimum and maximum airtemperature, precipitation, potential evapotranspiration andglobal radiation on a daily basis. The TNT2 model allowsfor several climate zones to be considered, in which case araster map of climate zones must be provided to the model.Here, only one climate zone is considered.

In total, the TNT2-P model includes 15 parameters foreach soil type, i.e. 30 parameters in total if two soil drainageclasses are considered. To reduce the number of model runsnecessary to explore the parameter space using Monte Carlosimulations, several parameters were given fixed values, or aconstant ratio between the two soil types was set (Table 1).In the hydrological sub-model, the parameters to vary wereidentified in a previous sensitivity analysis (Moreau et al.,2013). In the soil sub-model, all the parameters were varied.

Finally, only 12 parameters were varied independently(see Table 1). Initial parameter ranges for the hydrologicalsub-model were based on values from several previous stud-ies in western France (Moreau et al., 2013) and those for thesoil sub-model were based on a preliminary manual trial anderror procedure. The SRP concentration for deep flow water

Figure 3. Rating curve in Kervidy–Naizin; acceptability bounds de-rived from 90 % prediction interval (blue line: fitting regression;black dashes: 90 % prediction interval). Red dots represent the orig-inal discharge measurements used to calibrate the stage–dischargerating curve (Carluer, 1998).

was based on actual measurement of SRP in the weatheredschist (Dupas et al., 2015c). A constant flux value for do-mestic sources was set at the 1st percentile of the daily fluxbetween 2007 and 2013 (Dupas et al., 2015b).

2.3 Deriving limits of acceptability from datauncertainty assessment

The Monte Carlo-based GLUE methodology has beenwidely used in hydrology and is described elsewhere (Bevenand Freer, 2001b; Beven, 2006, 2009). Briefly, the rationaleof GLUE is that many model structures and parameter setscan give “acceptable” results, according to one or several per-formance measures. Hence, GLUE considers that all modelsthat give acceptable results should be used for prediction. Akey issue in GLUE is to decide on a performance thresholdto define acceptable models; typically, modellers set a thresh-old value of a measure such as the Nash–Sutcliffe efficiencybased on their subjective appreciation of data uncertainty oron previously used values. To allow for a more explicit jus-tification of the performance threshold values used, the lim-its of acceptability approach outlined by Beven (2006) relieson an assessment of uncertainty in the calibration/evaluationdata. According to this approach, all model realizations thatfall within the limits of acceptability are used for prediction,weighted by a score calculated based on overall performance.

Details on how the limits of acceptability for daily dis-charge and daily SRP load were derived from uncertainty as-sessment of the observational data are presented below. In-put data, such as weather and soil Olsen P data, also con-tained uncertainties that were not accounted for explicitly in



Table 1. Initial parameter ranges in the hydrological and soil phosphorus sub-models.

Abbreviation Unit Hydrological (H) or Range poorly Range well-phosphorus (P) drained soils drained soilsmodel (min–max) (min–max)

Lateral transmissivity at saturation T m2 day−1 H 4–8 →× 1.5Exponential decay rate of hydraulicconductivity with depth

m m2 day−1 H 0.02–0.2 0.02–0.2

Soil depth ho m H 0.3–0.8 →× 1Drainage porosity of soil po cm3 cm−3 H 0.1–0.4 →× 1Regolith layer thickness h1 m H 5–10 →× 4Exponent for evaporation limit A – H 8 (fixed) →× 1kRC parameter for capillary rise kRC – H 0.001 (fixed) →× 1n parameter for capillarity rise N – H 2.5 (fixed) →× 1Drainage porosity of regolith layer p1 cm3 cm−3 H 0.01–0.05 →× 1Background P release coefficient forsub-surface flow

CoefSRP overland – P 0–0.015 →× 1

Background P release coefficient foroverland flow

CoefSRP sub-surface – P 0–0.25 →× 1

Temperature coefficient 1 T1 – P 5–10 →× 1Temperature coefficient 2 T2 – P 2–10 →× 1Soil moisture coefficient S1 – P 0–2 →× 1SRP concentration in deep flow SRP_deep mg L−1 P 0–0.007 →× 1

the limits of acceptability due to a lack of data to quantifythem.

2.3.1 Discharge

Error in discharge measurement data was assessed from theoriginal discharge measurements used to calibrate the stage–discharge rating curve (Carluer, 1998). The rating curve usedin this study was

Q= a · (h−h0)b, (7)

where Q is discharge, h is stage reading, h0 is stage readingat zero discharge, a and b are calibrated coefficients. Limitsof acceptability were defined as the 90 % prediction intervalof log–log linear regression (Fig. 3). The acceptability rangeestimated in this way was ±39 % on average. This uncer-tainty interval is in the higher range of values found in otherstudies, e.g. Coxon et al. (2015), who found that mean dis-charge uncertainty was generally between 20 and 40 % in 500catchments of the United Kingdom. This relatively large un-certainty interval is due to the fact that it was derived from aprediction interval rather than a confidence interval (the 90 %confidence interval of the log–log linear regression would be14 % of the mean discharge value during the study period).A prediction interval is an interval in which future observa-tions will likely fall, whereas a confidence interval is an in-terval in which the mean of repeated observation will likelyfall. Because in the TNT2-P model’s evaluation we want eachobservation to fall in the acceptability interval (Sect. 2.3.3), aprediction interval was more appropriate. For daily discharge

values below 2 mm day−1, fixed acceptability limits were setat the 90 % prediction interval for a stage measurement cor-responding to 2 mm day−1.

2.3.2 SRP load

Uncertainty in “observed” daily load includes uncertainty indischarge (see Sect. 2.3.1) and uncertainty in SRP concen-tration. The acceptability limit for daily load was estimatedby the sum of relative uncertainty assessed for dischargeand SRP concentration (in percentage). Uncertainty in SRPconcentration stems from sampling frequency problems asone grab sample collected on a specific day is incommen-surable with the mean daily concentration or load simulatedby the model. Further, measurement errors exist that includethe effect of storage time (Haygarth et al., 1995). Duringbaseflow periods, measurement error was expected to be themain source of uncertainty because relative measurement er-ror was large for low concentrations, especially when sam-ple storage time exceeded 48 h (Jarvie et al., 2002), whereasconcentrations vary little. During storm events, sampling fre-quency was expected to be the main source of uncertaintybecause SRP concentration can vary by 1 order of magnitudewithin a few hours. Therefore, different acceptability limitswere set for both flow conditions. We considered storms asevents with > 20 L s−1 increase in discharge and the follow-ing 24 h.

During baseflow periods, the acceptability limits were de-rived from the 90 % prediction interval of a linear regressionmodel (y = a ·x+b) linking pairs of data points sampled onthe same day (reference sample between 16:00 and 18:00,



Figure 4. (a) Linear regression model linking the reference data and a verification data set; (b) measurement error as estimated froma repeatability test performed by the laboratory in charge of producing reference data (blue line: fitting regression; black dashes: 90 %prediction interval).

verification sample between 11:00 and 15:00) and analysedindependently (within a fortnight for the reference sampleand within 1–2 days for the verification sample). It was as-sumed that there was no systematic bias between the twodata sets due to different sampling time. The reference SRPconcentrations were on average 13 % lower than the verifica-tion value but this difference was not statistically significant(Mann–Whitney rank sum test, p > 0.05). This method en-compasses all various sources of uncertainty, which resultsin prediction intervals much wider than what would resultfrom a mere repeatability test; at the median concentration(0.02 mg L−1), the estimated prediction interval was 166 %with this method vs. 57 % with a repeatability test (Fig. 4).As for discharge estimates, the high percentage represents asmall absolute value (0.03 mg L−1) during baseflow periods.

During storm events, acceptability limits were derivedfrom the 90 % prediction interval of concentration dischargestatistical models (C = a ·Qb) using high-frequency au-tosampler data. Two reasons led us to use a statistical model(which also implies the assumption that errors are aleatoryand temporally independent): (i) the measurement uncer-tainty as assessed by the laboratory repetition test was an un-derestimate of the real uncertainty of autosampler data, be-cause it does not include other major sources of error suchas delayed filtration and sample decay during storage; (ii) itwas necessary to extrapolate the sub-daily observation to thedaily resolution of the model. The limits of this choice willbe discussed in Sect. 4.3. An empirical model was used tofit each storm event monitored separately and a delay termwas introduced manually in the empirical model when a timelag existed between concentration and discharge peaks. Theempirical models were then applied to extrapolate concentra-tion estimation during 2 days at 10 min resolution, for eachof the 14 storm events monitored. Finally the 2-day mean

Figure 5. Example of an empirical concentration – dischargemodel; acceptability bounds derived from 90 % prediction interval.Red circles represent the SRP measurements.

“observed” load was estimated as the mean of 10 min loadsand uncertainty limits were derived from the 90 % predictioninterval. In model evaluation, the mean of simulated loadsduring 2 consecutive days was evaluated against the 2-daymean “observed” load for which prediction intervals havebeen calculated. A 2-day acceptability limit enables all thestorm events to be covered (Fig. 5 and Supplement). A 2-dayaggregation was necessary here because increased SRP loadas a response to each storm event could occur either mainlyduring the day of the rainfall (if the rainfall occurred earlyin the morning) or mainly during the day following the rain-fall (if the rainfall occurred late in the evening), and with thedaily resolution of the input data and model simulation, theinformation about the timing of the rainfall event was notavailable to the model.

When comparing autosampler data with data from imme-diately filtered samples, the ratio obtained had the range 1–1.6 (mean= 1.3); hence, autosampler data were underesti-



Table 2. Starting and ending dates of periods studied.

Name Starting date Ending date

Autumn 2013 1 October 2013 31 December 2013Winter 2014 1 January 2014 31 March 2014Spring 2014 1 April 2014 31 July 2014Autumn 2014 1 October 2014 31 December 2014Winter 2015 1 January 2015 31 March 2015Spring 2015 1 April 2015 31 July 2015

mates of the true concentration, arguably through adsorptionor biological consumption. We used the mean ratio to cor-rect all storm acceptability intervals by 30 % and the rangevalues to extend the upper limit by 60 %. During days witha storm event not monitored at high frequency with an au-tosampler, we considered that the grab sample data did notcontain enough information to derive an acceptability inter-val for daily SRP load; hence, simulated load was not evalu-ated for events not monitored at high frequency.

2.3.3 Model runs and selection of acceptable models

To explore the parameter space, 20 000 Monte Carlo realiza-tions were performed to simulate daily discharge and SRPload during the water years 2013–2014 and 2014–2015. Thenumber of Monte Carlo realizations was constrained by thecomputation time required to run a spatially explicit modelin this catchment. A 7-month initialization period was runto reduce the impact of initial conditions on simulated re-sults during the study period, from 1 October 2013 to 31 July2015.

To be considered acceptable, model runs must fall withinthe acceptability limits defined in Sect. 2.3.1 and 2.3.2. Morespecifically, 100 % of simulated daily discharge, 100 % ofsimulated baseflow SRP load and 100 % of simulated stormSRP load have to fall within the acceptability limits. Thus,572 acceptability tests were performed for discharge, 378 forbaseflow SRP load and 14 for storm SRP loads, i.e. 964 eval-uation criteria.

To evaluate the model performance in more detail, nor-malized scores were calculated during six periods (Table 2).To calculate the scores, a difference was calculated betweeneach of the daily simulated discharge, baseflow SRP load and2-day storm SRP loads and the corresponding observation.This difference was then normalized by the width of the ac-ceptability limit defined for that day; therefore, the score hasa value of 0 in the case of a perfect match with observation,−1 at the lower limit and +1 at the upper limit (Fig. 6a). Fi-nally, the median of this ratio was calculated for each of thesix periods to investigate whether the model tended to un-derestimate or overestimate discharge and loads at differentmoments of the year and between the two years.

Model runs were successively evaluated for discharge,baseflow SRP load and storm SRP load. To use the models

Table 3. Sensitivity analysis of the model to 18 model parameters(insignificant “.”, important “∗”, critical “∗∗∗”). Parameters signifi-cations are detailed in Table 1.

Discharge Baseflow StormSRP load SRP load

T (poorly drained soils) . ∗∗∗ ∗∗∗

m (poorly drained soils) ∗∗∗ ∗∗∗ ∗∗∗

ho (poorly drained soils) ∗∗∗ ∗∗∗ .po (poorly drained soils) ∗∗∗ ∗∗∗ ∗∗∗

h1 (poorly drained soils) ∗∗∗ ∗∗∗ .p1 (poorly drained soils) ∗∗∗ ∗∗∗ ∗∗∗

T (well-drained soils) . ∗∗∗ ∗∗∗

m (well-drained soils) ∗∗∗ ∗∗∗ ∗∗∗

ho (well-drained soils) ∗∗∗ ∗∗∗ .po (well-drained soils) ∗∗∗ ∗∗∗ ∗∗∗

h1 (well-drained soils) ∗∗∗ ∗∗∗ .p1 (well-drained soils) ∗∗∗ ∗∗∗ ∗∗∗

Coef_sub-surface . ∗∗∗ .Coef_overland . ∗∗∗ ∗∗∗

SRP_deep . . .S1 . ∗∗∗ ∗∗∗

T 1 . ∗∗∗ ∗∗∗

T 2 . ∗∗∗ ∗∗∗

Figure 6. Normalized scores (a) and weighting function (b).

for prediction, each accepted model was given a likelihoodweight according to how well it has performed for each of the964 evaluation criteria. Here the statistical deviation weightwas used (truncated to 90 % prediction interval) (Fig. 6b). To“combine” the weights derived from the rating curve and theSRP concentration statistical models, a kernel density esti-mate (with Gaussian smoothing kernel) was computed to fit10 000 realizations of the multiplied error models. Calculatedweights were then averaged for discharge, baseflow SRP loadand storm SRP load respectively, and the final likelihood wascalculated as the product of all three averages.



The model’s sensitivity to each hydrological and soilparameter was performed with a Hornberger–Spear–YoungGeneralized Sensitivity Analysis (HSY GSA; Whitehead andYoung, 1979; Hornberger and Spear, 1981). For each eval-uation criteria (daily discharge, daily baseflow SRP loadand 2-day storm SRP load), the model runs were splitinto acceptable and non-acceptable runs according to theabove-mentioned acceptability limits. Then a Kolmogorov–Smirnov test was performed to assess whether the distribu-tion of each of the three evaluation criteria differs betweenacceptable and non-acceptable models for each parameter.Because the Kolmogorov–Smirnov test might suggest thatsmall differences in distribution are very significant whenthere are larger number of runs, this method is a qualitativeguide to relative sensitivity. The p value of the Kolmogorov–Smirnov test is used to discriminate whether the model iscritically sensitive (p < 0.01, “∗∗∗”), importantly sensitive(p < 0.1, “∗”) or insignificantly sensitive (p > 0.1, “.”) to eachparameter and for each of the three evaluation criteria.

In addition to the acceptability limit approach, a NSE (Mo-riasi et al., 2007) was calculated for daily discharge and dailyload and concentration to allow for a comparison with othermodelling studies where it has been taken as an evaluationcriterion.

3 Results

3.1 Presentation of observation data and calculation ofacceptability limits

The two water years studied were highly contrasted in termsof hydrology and SRP loads. The water year 2013–2014was the wettest in the last 10 years, with cumulative rain-fall of 1289 mm and cumulative runoff of 716 mm. Thewater year 2014–2015 was an average year (fifth wettestin the last 10 years), with cumulative rainfall of 677 mmand cumulative runoff of 383 mm. Annual SRP load was0.35 kg P ha−1 yr−1 in 2013–2014 and 0.17 kg P ha−1 yr−1 in2014–2015, i.e. a difference 10 % higher than that of dis-charge. Observed mean SRP concentration during the studyperiod was 0.024 mg L−1.

Figure 7a and b show acceptability limits for daily dis-charge and daily SRP loads. Note that acceptability limits fordischarge were calculated every day, while the acceptabilitylimits for SRP load was calculated on a daily basis duringbaseflow periods and on a 2-day basis during storm eventsmonitored at high frequency. No SRP load acceptability limitwas calculated during storm events when no high-frequencyautosampler data were available.

3.2 Model evaluation

First, model runs were evaluated against acceptability limitsdefined for discharge (Fig. 7c). A total of 5479 out of 20 000models fulfilled the selection criterion for discharge; i.e. they

had 100 % of simulated daily discharge within the accept-ability limits. The NSE estimated for these models rangedfrom 0.75 to 0.93. The normalized scores calculated season-ally (Fig. 8a) show that simulated discharge is often overes-timated in autumn and spring, and underestimated in winter.

Then, model runs were evaluated against acceptabilitylimits defined for SRP loads (Fig. 7d). During baseflow pe-riods, 4964 out of 20 000 models fulfilled the selection cri-terion for SRP loads; i.e. they had 100 % of simulated dailySRP load within the acceptability limits. Among them, 1595also fulfilled the previous selection criterion for discharge.Normalized scores for baseflow SRP load showed the sametrend as for discharge (Fig. 8b), i.e. overestimation in autumnand spring, and underestimation in winter. During stormevents, only seven models fulfilled the selection criterion forSRP loads; i.e. they had 14 out of 14 of simulated 2-daystorm SRP loads within the acceptability limits, but none ofthem fulfilled the selection criteria for discharge and base-flow SRP loads. Two storm events were particularly difficultto simulate (number 2 and number 9, Fig. 8c), probably be-cause their acceptability interval was very narrow as a re-sult of only small changes in discharge and concentration.To obtain a reasonable number of acceptable models, we re-laxed the selection criterion so that the acceptable modelshad to simulate 12 out of 14 of storm loads within the ac-ceptability limits, in addition to the selection criteria definedfor discharge and baseflow SRP load; 539 models were thenaccepted. Estimated NSE of these 539 models ranged from0.09 to 0.81 for daily load and from negative values to 0.53for daily concentrations (this includes all data from the regu-lar sampling).

3.3 Sensitivity analysis and prediction results

According to the HSY generalized sensitivity analysis, sim-ulated discharge was critically sensitive to 10 out of the 12hydrological parameters varied (Table 3). Simulated SRPload was critically sensitive to the sub-surface and overlandflow parameters during baseflow periods and to the overlandflow parameter during storm events. During baseflow peri-ods, SRP load was insignificantly sensitive to the parame-ter associated with deep flow load. Both baseflow and stormSRP loads were critically sensitive to the parameter relatedto soil moisture and soil temperature-dependent SRP solubi-lization (S1, T 1 and T 2), in addition to 12 and 8 hydrolog-ical parameters respectively. This identification of sensitiveparameters can be used in future application of the TNT2-P model in the study catchment, as suggested by Whiteheadand Hornberger (1984) and Wade et al. (2002b).

Figure 9 shows the daily discharge, SRP load and con-centration as simulated by the acceptable models. SimulatedSRP load during the water year 2013–2014 ranged from 0.81to 3.25 kg P ha−1 yr−1 (median= 1.68 kg P ha−1 yr−1);simulated SRP load during the water year 2014–2015 ranged from 0.14 to 0.73 kg P ha−1 yr−1 (me-



Figure 7. Acceptability limits for daily discharge (a) and SRP load (b). Blue lines represent best estimates; black lines represent the accept-ability limits. Storm loads acceptability limits are represented by vertical blue lines. An example of 50 model runs simulating discharge (c) anddaily load (d). Black vertical lines represent the starting and ending dates for each season (Table 2).

dian= 0.34 kg P ha−1 yr−1). Best estimate of SRP loadaccording to observation data was 0.35 kg P ha−1 yr−1 in2013–2014 and 0.17 kg P ha−1 yr−1 in 2014–2015. Ac-cording to the model, 49–55 % (median= 52 %) of waterdischarge and 66–70 % (median= 67 %) of SRP load oc-curred during storm events. Mean SRP concentrations duringthe two water years ranged from 0.014 to 0.044 mg L−1

(median= 0.029 mg L−1), whereas mean observed SRPconcentration was 0.024 mg L−1.

4 Discussion

4.1 Role of hydrology and biogeochemistry indetermining SRP transfer

The fairly good performance of TNT2-P at simulating SRPloads provides further support that the hydrological and bio-geochemical processes included into the model are dominantcontrolling factors in the Kervidy–Naizin catchment (i.e. themodelling hypotheses could not be rejected based on theseresults, except for two storm events). The primary controlof hydrology in controlling connectivity between soils andstreams has been highlighted by many studies analysing wa-ter quality time series at the outlet of agricultural catchments(Haygarth et al., 2012; Jordan et al., 2012; Dupas et al.,2015c; Mellander et al., 2015). This modelling exercise also

provides further support that SRP solubility can be satisfac-torily represented by the soil Olsen P content and could varyaccording to temperature and moisture conditions. The un-derlying processes have not been identified precisely in theKervidy–Naizin catchment; independent laboratory experi-ments have shown that microbial cell lysis resulting from al-ternating dry and water-saturated periods in the soil could bethe cause of increased SRP mobility (Turner and Haygarth,2001; Blackwell et al., 2009). This could explain the mois-ture dependence of SRP solubility in the model. Furthermore,net mineralization of soil organic phosphorus could explainthe temperature dependence of SRP solubility in the model.These two hypotheses may explain increased SRP solubilityin soils in periods of dry and hot conditions and will be fur-ther explored by incubation experiment with soils from theKervidy–Naizin catchments.

4.2 Potential improvements to the model structureaccording to modelling purpose

The TNT2-P model was designed to test hypotheses aboutdominant processes and for this purpose, a parsimoniousmodel structure was chosen to include only the processes thatwere to be tested. This parsimonious model structure mightcontain some conceptual misrepresentations due to oversim-plification, and it might not include all the processes nec-



Figure 8. Normalized score for daily discharge (a), baseflow SRP load (b) and storm SRP load (c).

essary for the purpose of evaluating management scenarios.This section discusses whether the simplifications made areacceptable in the context of different catchment types, andto which conditions the model could be made more complexby including additional routines for the purpose of evaluatingmanagement scenarios.

From a conceptual point of view, the lack of cell-to-cellrouting of SRP fluxes might result in erroneous results insome contexts. The fact that all the SRP emitted from eachcell through overland flow and sub-surface flow reaches thestream on the same day is generally acceptable for the catch-ment studied, because groundwater interception of shallow

soil layers occurs in the riparian zone only; hence, the signalof SRP mobilization in these soils is generally transmitted tothe stream (Dupas et al., 2015c). This simplification, how-ever, does not seem to be acceptable for all the storm eventsin the study catchment, as the SRP load evaluation criteriahad to be relaxed to obtain acceptable model results. It wouldalso not be acceptable in catchments where soil–groundwaterinteractions are taking place throughout the landscape, e.g.due to topographic depressions or poorly drained soils. Inthe latter type of catchment, transmission of the SRP mobi-lization signal to the stream is more complex (Haygarth et



Figure 9. Median and 95 % credibility interval for daily discharge (a), SRP load (b) and SRP concentration (c). Red circles representobservational data.

al., 2012); hence, a more complex model structure would berequired.

The reason for this simplification was that we lackedknowledge of SRP re-adsorption in downslope cells (or onsuspended sediments in the stream network) and on the long-term fate of re-adsorbed SRP. For a more physically realisticrepresentation of processes, it is likely that an explicit rep-resentation of flow velocities and pathways would be nec-essary, along with an explicit representation of several soilP pools. However, such an explicit representation of pro-cesses contradicts the idea of a parsimonious model, whichwas adopted here for the purpose of identifying dominantprocesses. In this respect, TNT2-P is an aggregative modelrather than a fully distributed model although it is based on afully distributed hydrological model (Beaujouan et al., 2002).The current spatial distribution allows for finer representationof soil–groundwater interactions (i.e. the time-varying ex-tent of the riparian wetland area) than semi-distributed mod-

els such as SWAT (Arnold et al., 1998), INCA-P (Wade etal., 2002a) and HYPE (Lindstrom et al., 2010) but at highercomputational cost. It would be interesting to test to what ex-tent moving from an aggregative model with fully distributedinformation to a semi-distributed model would degrade themodel performance while reducing computational cost. Thiscould be achieved by grouping cells according to a hydro-logical similarity criterion like in the Dynamic TOPMODEL(Beven and Freer, 2001a; Metcalfe et al., 2015) and do thesame for similarity in soil P content. Reducing computationtime is critical in the context of a GLUE analysis becausethis method requires the parameter space to be sampled ade-quately to identify those models to be considered acceptable.This is debatable here because 12 parameters were varied andonly 20 000 model runs were performed. It is therefore possi-ble that some regions of the parameter space with acceptablemodels might not have been sampled.



If reducing the number of calculation units proved to re-duce computational cost without degrading quality of predic-tion, it would be possible to include more parameters in themodel, for example to simulate SRP re-absorption in downs-lope cells or include routines to simulate the evolution of soilP content under different management scenarios (Vadas etal., 2012), and still perform a Monte Carlo-based analysis ofuncertainty. The question of coupling or not coupling sucha soil P routine with the current TNT2-P model will dependon available data and on the length of available time series;studying the evolution of the soil P content requires at leasta decade of soil observation data (Ringeval et al., 2014) andprobably a longer period of stream data to account for thetime delay for a perturbation in the catchment to becomevisible in the stream (Wall et al., 2013). Thus, the 2 yearsof daily stream SRP in the Kervidy–Naizin catchment arenot enough to build a coupled soil–hydrology model with anelaborate soil P routine. Therefore, as things stand, it is morereasonable to generate new soil Olsen P maps with a separatemodel such as the APLE model (Vadas et al., 2012; Benskinet al., 2014) or the “soil P decline” model used by Wall etal. (2013), and use these maps as input to TNT2-P.

Because the current model can simulate response to rain-fall, soil moisture and temperature, it could be used to testthe effect of climate scenarios on SRP transfer. In westernFrance, and more generally in western Europe, the climatefor the next few decades is expected to consist of hotter,drier summers and warmer, wetter winters (Jacob et al., 2007;Macleod et al., 2012; Salmon-Monviola et al., 2013) withincreased frequency of high-intensity rainfall events (De-qué, 2007). In these conditions, SRP concentrations and loadwill seemingly increase compared to today’s climate as aresult of both an increase in SRP solubility in soil due tohigher temperatures and more severe drought, and an in-crease in transfer due to wetter winters and more frequenthigh-intensity rainfall events. TNT2-P could be used to con-firm and quantify the expected increase in SRP transfer fromdiffuse sources in future climate scenarios, and to determinewhether those predicted changes are significant relative to theuncertainty in predictions under current climate variability.

4.3 Improving information content in the data

Despite relatively large uncertainty in the data used in thisstudy, it was possible to build a parsimonious catchmentmodel of SRP transfer for the purpose of testing hypothe-ses about dominant processes, namely the role of hydrologyin controlling connectivity between soils and streams and therole of temperature and moisture conditions in controllingsoil SRP solubilization. However, the large uncertainties inthe calibration data lead to large prediction uncertainty. Forexample, the SRP load estimated by the behavioural modelsfrom 2013 to 2015 ranged from 0.48 to 1.99 kg P ha−1 yr−1;hence, the width of the credibility interval was 150 % of themedian (1.0 kg P ha−1 yr−1). Similarly, the mean SRP con-

centration estimated by the behavioural models from 2013to 2015 ranged from 0.014 to 0.044 mg L−1; hence, thewidth of the credibility interval was 102 % of the median(0.029 mg L−1). The large uncertainty in the calibration data,along with a lack of long-term information, also prevents in-cluding more detailed processes in the soil routine.

To reduce uncertainty in prediction and to build more com-plex models, several options exist to improve informationcontent in the data. As stated by Jackson-Blake and Star-rfelt (2015), “the key to obtaining a realistic model simula-tion is ensuring that the natural variability in water chemistryis well represented by the monitoring data”. The monitor-ing strategy adopted in the Kervidy–Naizin catchment shouldtheoretically enable one to capture the natural variability instream SRP concentration, because sampling took place dur-ing two contrasting water years, during different seasons andat a high frequency during 14 storm events. The analysisof uncertainty in the data shows that a large part of uncer-tainty in “observed” SRP concentration originates from sam-ple storage, both unfiltered between the time of autosam-pling and manual filtration and between filtration and anal-ysis. This is due to SRP being non-conservative. Thus, thereis room for improvement in reducing storage time, withoutfurther increasing the monitoring frequency. In this respect,the primary interest of investing in high-frequency banksideanalysers would lie in their ability to analyse water samplesimmediately in addition to providing near-continuous data.Because bankside analysers perform measurements in rela-tively homogeneous conditions, unlike the manual and au-tosampler data for which storage time of filtered and unfil-tered samples vary, a finer quantification of uncertainty inthe measurement data would be possible (e.g. Lloyd et al.,2016).

Finally, alternative methods to statistical models could beused to derive acceptability limits (in this study three statis-tical models are used: the rating curve, the SRP concentra-tion uncertainty during baseflow periods and the storm eventinterpolation model) because statistical models have at leastthree shortcomings: (i) they lump the uncertainty linked tothe timing of sampling, the immediate or delayed filtration ofthe samples, the storage time and the analytical error; (ii) theformula chosen adds error to the already existing measure-ment errors because empirical models are not perfect repre-sentations of the system dynamics; (iii) they assume a para-metric distribution and temporally independent errors, whichare not always verified in practice. As an alternative, non-parametric methods could be used, but these methods gener-ally require a large number of data points and they are notsuitable for extrapolation to extreme values.

5 Conclusion

The TNT2-P model was capable of capturing daily variationof SRP loads, thus confirming the dominant processes identi-



fied in previous analyses of observation data in the Kervidy–Naizin catchment. The role of hydrology in controlling con-nectivity between soils and streams, and the role of soil OlsenP, soil moisture and temperature in controlling SRP solubil-ity have been confirmed. The lack of any representation ofthe short-term effect of management practices did not seemto reduce the model’s performance. Their long-term effecton the soil Olsen P could be simulated with an independentmodel or through an additional sub-model if a longer periodof data was available to calibrate it. The modelling approachpresented in this paper included an assessment of the infor-mation content in the data, and propagation of uncertainty inthe model’s prediction. The information content of the datawas sufficient to explore dominant processes, but the rela-tively large uncertainty in SRP concentrations would seem-ingly limit the possibility for including more detailed pro-cesses into the model. Data from the near-continuous bank-side analyser will probably allow for calibrating more de-tailed models in the near future.

6 Data availability

Data of “ORE AgrHyS” can be downloaded from http://www6.inra.fr/ore_agrhys/Donnees (ORE AgrHyS, 2015).

The Supplement related to this article is available onlineat doi:10.5194/hess-20-4819-2016-supplement.

Acknowledgements. This work was funded by the “Agence del’Eau Loire Bretagne” via the “Trans-P project”. Long-termmonitoring in the Kervidy–Naizin catchment is supported by “OREAgrHyS”.

Edited by: J. FreerReviewed by: T. Krueger and P. G. Whitehead

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